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Everything about Permutation
Mathematical version of an order change
In mathematics, a permutation is a bijective function of a finite set onto itself. When the set is represented as an ordered sequence of its members, a permutation amounts to change the place of the members of the set: if f is a permutation, is the new place of the ith member of the sequence. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: PermutationA 5-minute orientation
- Skim a recent paper: Image encryption algorithm based on a 2D-CLSS hyperchaotic map using simultaneous permutation and diffusionInfluential work since 2022
- Pick up a classic book: Combinatorics of PermutationsThe most-reprinted book on the subject
- Read the landmark paper: Nonparametric permutation tests for functional neuroimaging: A primer with examplesCited 5,853 times
- Go sideways: Lehmer codeA closely related topic
- Go sideways: Parity of a permutationA closely related topic
📖 Definitions
Noun One of the ways something exists, or the ways a set of objects can be ordered.
Noun A one-to-one mapping from a finite set to itself.
Noun An ordering of a finite set of distinct elements.
Noun A transformation of a set's prime form, by applying one or more of certain operations, specifically, transposition, inversion, and retrograde.
🏆 Landmark papers (most cited)
Nonparametric permutation tests for functional neuroimaging: A primer with examples
CLUMPP: a cluster matching and permutation program for dealing with label switching and multimodality in analysis of population structure
Permutation Entropy: A Natural Complexity Measure for Time Series
Permutation inference for the general linear model
Permutation importance: a corrected feature importance measure
Permutation tests for univariate or multivariate analysis of variance and regression
Comparing network structures on three aspects: A permutation test.
Implementing a Class of Permutation Tests: The coin Package
🆕 Influential since 2022
Image encryption algorithm based on a 2D-CLSS hyperchaotic map using simultaneous permutation and diffusion
Random Permutation Set
An Improved Artificial Bee Colony Algorithm With Q-Learning for Solving Permutation Flow-Shop Scheduling Problems
Efficient multi-objective meta-heuristic algorithms for energy-aware non-permutation flow-shop scheduling problem
A robust Spearman correlation coefficient permutation test
📚 Books worth reading
- 📕Combinatorics of PermutationsMiklos Bona · 2004
Choice and chanceWilliam Allen Whitworth · 1870- 📕Permutation tests for complex dataFortunato Pesarin · 2010
Lehrbuch der CombinatorikEugen Netto · 1901
Combinatory analysisPercy Alexander MacMahon · 1915
The Sundae ScoopStuart J. Murphy, Stuart Murphy · 2002
Representations of solvable groupsOlaf Manz · 1993
Combinatorics of permutationsMiklós Bóna · 2004
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Lehmer code In mathematics and in particular in combinatorics, the Lehmer code is a particular way to encode each possible permutation of a sequence of n numbers.…
- Parity of a permutation In mathematics, when X is a finite set with at least two elements, the permutations of X (that is, the bijective functions from X to itself) fall into…
- Inversion (discrete mathematics) In computer science and discrete mathematics, an inversion in a sequence is a pair of elements that are out of their natural order. Let π be a permutation…
- Cyclic permutation In mathematics, and in particular in group theory, a cyclic permutation is a permutation consisting of a single cycle. In some cases, cyclic permutations…
- Random permutation A random permutation is a sequence where any order of its items is equally likely at random, that is, it is a permutation-valued random variable of a set…
- Steinhaus–Johnson–Trotter algorithm The Steinhaus–Johnson–Trotter algorithm or Johnson–Trotter algorithm, also called plain changes, is an algorithm named after Hugo Steinhaus, Selmer M.…
- Permutation group In mathematics, a permutation group is a group G whose elements are permutations of a given set M and whose group operation is the composition of permutations…
- Fisher–Yates shuffle The Fisher–Yates shuffle is an algorithm for shuffling a finite sequence. The algorithm takes a list of all the elements of the sequence, and continually…